Algorithmic trading system and method

ABSTRACT

A system and method for allowing market participants to evaluate the likelihood of finding hidden volume. The model can predict hidden volume and assess the probability that a market order will be executed within the spread and better than the mid-quote. The cost per immediate execution can be assessed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation of and claims priority to U.S. patentapplication Ser. No. 11/812,359, filed Jun. 18, 2007, which claimedpriority to provisional application Nos. 60/814,066, filed Jun. 16, 2006and 60/944,131, filed Jun. 15, 2007, the entire contents of each ofwhich are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to systems and methods foridentifying liquidity. In particular, the present application relates tosystems and methods for determining the presence of hidden limit ordersin an order book.

2. Description of the Related Art

There is a demand among financial traders for more transparency andcurrency of market information in order driven electronic markets, suchas the new level 2 and real-time data products offered by NASDAQ andNYSE. Markets which provide electronic limit order books, including, forexample, Euronext, London Stock Exchange, XETRA, Spanish Stock Exchange,and Toronto Stock Exchange, provide a measure of currency andtransparency. An electronic limit order market is a trading platformwhere anonymous buyers and sellers post price-quantity pairs—i.e., thequoted bid (or ask) prices and associated quantities (depths) of a stockthat the market participant is willing to buy (or sell). Limit orderbooks offer market participants the ability to observe levels of marketliquidity by displaying prices and quantities of unexecuted limitorders. Utilizing this data, market participants can implement a rangeof “game theoretical” strategies and choose limit orders with specifiedprice, quantity, and timing, thus allowing them to minimize executioncosts and uncertainty, hide market information, and possibly move themarket towards the desired price.

Given concerns associated with information leakage due to orderplacements, some market venues allow market participants to enter“hidden” limit orders which do not reveal the full share volume sizeand/or the associated price level (also known as “iceberg”,“undisclosed”, or “discretionary” limit orders). This brings with it acomplex interrelationship between exposure risk (adverse selection),market liquidity, and the need for transparency. From a market designpoint of view, hidden limit orders represent a trade-off betweenliquidity and transparency. Trading systems need to attract liquidityand trading activity. The availability of hidden limit orders encourageslimit order traders, who are otherwise hesitant to fully disclose theirtrading interests, to supply liquidity—thus increasing the liquidity onthe system. However, hidden limit orders volume, by its nature, does notadd information to the market and thus, does not help in the market'stransparency.

In particular, hidden orders inside the spread will not attract activityto a venue, since most order routing systems can only operate on visible(i.e., displayed) information. Thus, as reported by ANANTH MADHAVAN,“Market microstructure: a survey”, Journal of Financial Markets, 3(2000), pp. 205-258, hidden limit orders clearly diminish supposedbenefits of transparent order driven markets: price efficiency, lowcosts of market monitoring and less information asymmetries.

The concept of hiding transaction fingerprints has been around forseveral years, but has recently seen increased popularity due to theadvent of algorithmic trading systems such as ITG's “Dark Server” orCSFB's “Guerilla,” which utilize continuous mid-point crosses from “DarkBooks.” For illiquid stocks, which have larger intra-day volatility, theconcept of hiding allows the market participant to transact with minimummarket impact.

Hidden limit orders have become an important limit order type. Asdisclosed in Hasbrouck and Saar [2002], hidden orders account for morethan 12% of all orders executed on Island, and Tuttle [2002] reportsthat hidden liquidity represents 20% of the inside depth in the Nasdaq100 stocks. D'Hondt, De Winne, and Francois-Heude [2004] disclose thathidden depth on Euronext Paris accounts for 45% of the total depthavailable at the best five quotes and 55% of the total depth at the bestlimits.

These findings suggest that there are underlying factors that cause amarket participant to use a hidden versus a visible limit order,considering the controversial rationale behind using hidden limitorders. Consistent with previous literature, there are two main beliefsfor the existence of hidden limit orders. First, hidden limit orders canbe used by large liquidity traders to reduce their exposure risk byhiding their intent to trade. In other words, liquidity traders usehidden limit orders as a self-protective strategy against other moreinformed traders. Second, hidden limit orders can be mostly submitted byinformed traders to conceal their insider information. By placing(aggressive) hidden limit orders, market participants with insiderinformation can trade quickly and almost unobserved. Therefore, informedtraders may prefer using undisclosed versus displayed limit orders forcertain market conditions.

Taking into account undisclosed limit orders can dramatically change thepicture of the limit order book at any given time of the day. Forexample, referring to FIG. 1, it can be easily concluded that ifinstantaneous execution of a buy market order for 1,000 shares ofcompany Argonaut Group Inc. is desired, the cost associated with thattrade (benchmarked on the existing mid-quote) would be $0.05 per share.This cost is computed by first assuming that only the observable volumeis available and then climbing up the book to pay the following averageexecution price x:

$\begin{matrix}{x = \frac{{500 \times 35.05} + {300 \times 35.07} + {( {1000 - ( {500 + 300} )} ) \times 35.12}}{1000}} \\{{= 35.06537},}\end{matrix}$giving a cost per share y of:

$\begin{matrix}{y = {35.07 - {{mid}\mspace{14mu}{quote}}}} \\{= {35.07 - 35.02}} \\{= {0.05.}}\end{matrix}$However, if the order book could be reconstructed in a way that includedthe inferred hidden shares using information from prevailing marketconditions, one would then see that the “true” cost for the 1,000 sharesis actually only about $0.045 per share:

$\begin{matrix}{x = \frac{\begin{matrix}{{3 \times 35} + {2 \times 35.01} + {5 \times 35.02} + {6 \times 35.03} +} \\{{543 \times 35.05} + {300 \times 35.07} + {141 \times 35.12}}\end{matrix}}{1000}} \\{= {35.06537.}}\end{matrix}$Thus, the cost per share y after hidden volume is considered is:

$\begin{matrix}{y = {35.06537 - {{mid}\mspace{14mu}{quote}}}} \\{= {35.06537 - 35.02}} \\{= {0.04537.}}\end{matrix}$

A trader seeing the “true” limit order book instead of FIG. 1 might bewilling to consider the opportunity cost relative to the market dynamicsassociated with removing only a portion of the desired volume fromwithin the spread—which leads to improvement in per share transactioncost. As reported by Pascual and Veredas [2004], the explanatory powerof the book is concentrated within the dynamics associated with thevisible best quotes. This trader would also be able to evaluate theprobability that an order is filled within or below the existing visiblebest ask price.

Thus, there remains a need for a system that can estimate hidden limitorders and provide a probabilistic “reconstructed” order book includinginferred hidden limit orders that allow the trader to factor thisinformation into a trading position.

SUMMARY OF THE INVENTION

According to an embodiment of the present invention, a system and methodare provided for identifying hidden liquidity. Systems and methods areprovided that determine the probability of the existence of hiddenliquidity, including a calculation of the volume of the hidden liquiditybetween the best bid and ask, and a prediction of the actual location(price) of the hidden volume. With this information, a complete limitorder book may be constructed and displayed that includes the expectedhidden volume at the appropriate price levels.

According to embodiments of the present invention, systems and methodsare provided for inferring the presence of hidden limit orders in anorder book based on historical order data. For example, lever 2 messagescan be examined within a predetermined time frame to identifycancellation or modification order messages that correspond in price,size and exchange to a particular trade. If a trade cannot be matched toa limit order message, the trade is classified as a hidden trade.

According to embodiments of the present invention, a model can beconstructed that predicts the volume and price (“location”) of hiddenliquidity for trading forums and/or for tradable assets (e.g., asecurity). The model is constructed from historical order information,which is used to infer hidden order volume and location from displayedorder and execution data. The model can consist of a number ofcoefficients associating hidden volume and/or location for each tradableasset with market conditions. Accordingly, the coefficients can be usedto estimate current hidden liquidity for a tradable assets based uponcurrent market conditions.

Models can be built from an examination of historical data and thenapplied to current data to predict the existence of hidden orders (e.g.,non-displayed limit orders) within a trade forum. An order book can bereconstructed that comprises both displayed and hidden order data.

According to embodiments of the present invention, hidden liquidity isestimated based on historical data, such as, 21-day median trade sharevolume.

Further applications and advantages of various embodiments of thepresent invention are discussed below with reference to the drawingfigures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graphic depiction of a limit order book for an exemplarystock.

FIG. 2 is a graph depicting exemplary hidden order volume modelcoefficient and parameter estimates by liquidity group.

FIG. 3 is a graph depicting exemplary hidden order location modelcoefficient and parameter estimates by liquidity group.

FIG. 4 is a graph depicting the probability that an undisclosed selllimit order is with a particular region of the bid-ask spread.

FIG. 5 is a graph depicting a reconstructed limit order book.

FIG. 6 is a graph depicting an average execution price as a function oftime.

FIG. 7 is a logical schematic diagram for a computer system that canimplement features of the present invention.

FIG. 8 is a flow chart depicting a method in accordance with anembodiment of the invention.

FIG. 9 is a flow chart depicting a method to develop and evaluate amodel of hidden order placement according to an embodiment of thepresent invention.

FIG. 10 is a flow chart depicting a method to evaluate a model forinferring hidden orders according to an embodiment of the presentinvention.

FIG. 11 is a flow chart depicting a method to develop and evaluate amodel of hidden order volume according to an embodiment of the presentinvention.

FIG. 12 is a flow chart depicting a method to develop a model forinferring hidden orders according to an embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

While the present invention may be embodied in many different forms, anumber of illustrative embodiments are described herein with theunderstanding that the present disclosure is to be considered asproviding examples of the principles of the invention and such examplesare not intended to limit the invention to the embodiments shown ordescribed herein.

According to one aspect of the invention, reconstruction of a limitorder book around the best levels allows measurement of the “true”execution prices if market orders or marketable limit orders are placed.The possibility of getting better than expected execution prices has twomain implications:

-   -   quantifying best execution (ignoring execution improvement can        be misleading when comparing execution quality across markets        with significant non-displayed additional liquidity); and    -   undisclosed (e.g., “hidden” or non-displayed) volume is an        integral part of the pricing process. It will be seen that price        improvement is largest when spreads are narrow and volatility is        large. Trader behavior is better understood relative to        additional information in the limit order book. The findings are        of great interest not only in terms of modeling pure order        driven markets and characterizing traders' behavior, but also in        giving an advantage as it relates to implementing an automatic        search (liquidity and asymmetric information) algorithm. For        more on some basic questions of pre-trade transparency and the        challenges faced when developing better trading algorithms and        improving trading performance see Borkovec and Yang [2005],        Domowitz and Yegerman [2005a], Yang and Jiu [2006], and Domowitz        and Yegerman [2005b]. Madhavan [2000, page 234] defines        pre-trade transparency as “the wide dissemination of current bid        and ask quotations, depths, and possibly also information such        as the existence of large order imbalance.”

Aspects of preferred embodiments of the present invention are describedas follows. The data are described in the section entitled “Data.”Static empirical evidence associated with hidden volume and itsplacement is described in the section entitled “Model.” Construction ofa limit order book with inferred hidden limit orders and applicationsare discussed in the section entitled “Applications.”

Data

The following explanation of the data includes a description of dataused by the inventors in developing aspects of the present invention.The data is exemplary in nature and the invention is not limited to thespecific data described. One skilled in the art will readily understandfrom the following discussion how to make or use the present invention.

Research data included three months of Comstock level 2 (L2) real timeinformation from ARCA (note that other suitable data sources areavailable, such as, for example, INET direct exchange Level 2 data). Twomonths of data from Jun. to Jul. 2005 were used to estimate theempirical models. Aug. 2005 data were used for out-of-sample testing.

Data feeds are made up of a series of sequenced messages that describeorders added to, removed from and executed on the correspondingexchange. In general, an “add order message” indicates that a new orderhas been accepted by the system and added to the displayed limit orderbook. The “modify order message” references a previously submitted orderthat has been partially executed (number of shares always reduced). A“cancel order message” is sent whenever an order on the book iscancelled; in the case of an Archipelago feed, this message meanscancelled or executed. Messages from INET include an “executionmessage,” which is sent whenever an order on the book is executed inwhole or in part, and a “trade message,” which provides informationabout execution events that involve orders not visible on the INET book.

In the case of an Archipelago feed, Level 1 trade messages must bematched with modify and cancel order messages to determine (1) whichorders have been executed or actually cancelled, and (2) which tradeshave been executed through undisclosed limit orders. To match tradeswith limit orders, L2 messages can be examined within a 2-second timebandwidth to find the order cancellation or modification message whichcorresponds in price, size, and exchange to a particular trade. If atrade is matched to an order message, the side classification of thistrade is obtained from the message; such trades would be classified asbeing visible.

If there is more than one match, it is assumed that the correct match isthe one which is closest in absolute time difference between the timestamp and the message time. If a trade cannot be matched with a limitorder message, then the trade can be classified as a hidden trade (i.e.,coming from a hidden/undisclosed limit order). To determine the side ofthe hidden trade, a generalization of the algorithm disclosed in CHARLESLEE AND MARK READY, “Inferring Trade Direction from Intraday Data”, TheJournal of Finance, 46(2) (1991), pp. 733-746, the contents of which arehereby incorporated by reference, can be used. The level of reliabilityfor the side classification algorithm was found to be 90-95% accuratewhen tested against execution data where the side is known.

Table 1 below contains a summary of exemplary trading data based on datafrom Comstock's ARCA data feed on 329 tickers from June-August 2005.Table 1 discloses the tickers used in the model, based on marketcapitalization. More than 78% of the tickers chosen belong to small capstocks, 13% belong to median cap stocks, and the remaining 9% belong tolarge cap stocks. A stock is defined as being small cap if its marketcapitalization is less than $1.5 billion. If the market capitalizationis greater than $1.5 billion but less than $10 billion, it is consideredas a median cap stock. All other stocks are classified as large capstocks.

For each large cap stock, the average number of trades per day as shownis 7,900 with an average trade size of 920 shares. The average number oftrades per day for each small cap stock is approximately 280 trades withan average trade size of 520 shares. Of the trading activities for thesmall cap stocks, 28% of all traded volume is classified as hidden,while the number is only 21% for the large cap stocks. Approximately 96%of all orders added to the book are eventually cancelled. Of thecancelled orders, approximately 10% can be classified as fleeting orders(i.e., defined as an order which is added and cancelled from the bookwithin 2 seconds or less). Order time stamps are generally in 1-secondincrements.

The data also show that, on average, hidden orders have a larger size incomparison to orders that are fully displayed. This result is consistentwith Harris'[1996] findings that traders often restrict displayedorders, especially for orders with larger expected remainders.

TABLE 1 LARGE MID CAP SMALL CAP STOCKS ($10 CAP STOCKS BILLION < STOCKSCHARACTERISTIC (CAP > $10 CAP < $1.5 (CAP < $1.5 (DAILY AVERAGE)BILLION) BILLION) BILLION) TRADES: Number of Trades 207,000 87,80072,000 Size of Trade (Visible) 370 300 200 Size of Trade (Hidden) 550450 320 Percentage of 21% 23% 28% Trade Hidden FLEETING/ CANCELLATION:Number of 328,500 126,800 160,100 Fleeting Orders Fleeting Orders/ 11% 9% 13% Total Cancelled Orders Cancelled Orders/ 96% 96% 97% Total AddedOrders Number of Stocks 26 43 260

Given that the model is trade-based in nature, classifying stocks bymarket capitalization is inadequate since stocks within the same marketcap group can differ significantly in trade volumes. Therefore, insteadof the commonly used market capitalization, stocks can be grouped basedon their 21-day median trade share volume. As a result, stocks can beclassified with similar trade volume within the same group.

To get a representative sample of tickers across the universe, allavailable tickers (approximately 7,000) can be ranked according to their21-days median trade volume at the beginning of the sample period. Then,this universe can be divided into eleven liquidity groups with LiquidityGroup 0 representing the least liquid stocks and Liquidity Group 10representing the most liquid stocks. For each of the eleven liquiditygroups, a randomly selected sample of tickers is used in the pooled datamodel. Loosely speaking, micro cap stocks belong to Liquidity Groups 0to Liquidity Group 4, small cap stocks belong to Liquidity Group 4 toLiquidity Group 7, mid cap stocks belong to Liquidity Group 8 toLiquidity Group 9, and large cap stocks belong to Liquidity Group 10.

This grouping is justified by examination of order placement in eachliquidity group showing that there is a clear difference in how limitorders are placed across different liquidity groups. Limit orderplacement can be classified into three categories: (1) AT, whichrepresents limit orders being placed at the best level, (2) BETTER,which represents limit orders being placed between best bid and ask, and(3) AWAY, which represents orders being placed at prices worse than thebest levels.

From FIG. 2 it can be seen that the placement pattern is not similaracross any liquidity group. For the lowest liquidity group, more than28% of all new limit orders were placed AT the best bid and ask levelwhile for the most liquid group, 48% of all new limit orders were placedAT the best bid and ask level. The difference in percentage reflects thedifferences in share trade volume, urgency to get order completed, andthe competition within the liquidity group.

In this pooled data analysis, specific factors that appear to affect theprobability of hidden order placement are identified. One intuitivehypothesis is that hidden orders are more frequently used for stockswith a high exposure risk (Harris [1997]).

In a market with low volatility, hidden orders may reduce the chances ofbeing front-run and thus volatility may play an active role in ananalysis. In a market that enforces time precedence, front-running canbe very expensive.

Since front-running is expected to be more expensive for stocks withrelatively low prices, the use of hidden orders is expected to be higherfor those stocks. As for uninformed traders, the option value of limitorders is affected by factors like volatility (Mid-Quote Volatility),trading activity (Depth Size, Time Since Last Trade, and Spread) andtime to total (partial) execution. Order exposure risk may also berelated to the expected time for an order to be (totally) executed andthe frequency of orders that are partially displayed is related to thetrading frequency of a stock.

Time of the day is another important variable, as there may beprivileged periods over the trading day to enter hidden orders on themarket. Market participants may place limit orders at specific periodsof the day. The model could be extended to capture the anomaliesassociated with days of the week and month of the year. The model couldalso be extended to take care of timing associated with rebalancingportfolios. The trading day can be divided into thirteen 30-minute timebins and the order placement pattern examined.

As shown in FIG. 3, time of day seems to explain where an order might beplaced. At the opening of the market, with no real information, a marketparticipant might be equally likely (33%) to place a limit order BETTER,AT, or AWAY. As the day progresses, for example, by 3:30-4:00 pm, theprobability that a market participant will place a limit order withinthe best bid and ask drops to 18%. The average number of limit ordersper ticker placed throughout the day shows that most limit orders areplaced at the first 2.5 hours of the trading day. This pattern isconsistent across all liquidity groups.

When the pattern associated with the number of the orders placed basedon the time period of the day is examined, one will note that it seemsto mimic the spread curve. This suggests that time bin might not be afactor associated with limit order placement and that what is observedis really limit order placement relative to the spread. The spread alsocaptures the market impatience and is possibly the first hint that theremight be asymmetric information among the market players. Glosten[1987], Glosten and Harris [1988], George, Kaul, and Nimalendran [1991],Brockman and Chung [1999] consider decomposition of bid-ask spread.

Glosten and Milgrom [1985] is among the many papers that identify thatinformation asymmetries among investors influence the bid-ask spread.Large spreads would seem to suggest that there is little or no marketinformation or activity. If the commonly known spread profile isexamined, the spread is, on average, the largest at the opening of themarket (the information searching period) and, as the day progresses andinformation is captured through the market transactions, the spreaddeclines and reaches its lowest level by the end of the trading day.

A hidden volume predictor may take all the previously discussedvariables or a subset into consideration. Some of these variablesdescribe the stock price dynamics, while others describe the“fundamental” or historical characteristics of the stock. The nextsection discusses in more detail the model and its associated inputvariables.

Dynamic variables can include “Spread,” which captures the level oftrade interest and can hint that there may be asymmetric informationamong the market players; “Mid-Quote Volatility,” where high volatilityreflects the market uncertainty and the possibility of hidden volumebeing executed away from the mid-quote; “Average 1st Level Depth (byside),” which provides a first idea about available liquidity inside thespread and possible market asymmetry; “Order Placements/Cancellations,”which signifies the intensity of information arrival to the market;“Lagged Hidden Volume,” in which the state of the trading world isrelated to what was previously observed and the level of dependency isrelated to the time that has elapsed since the last observed activity;and “Misalignment of the exchange mid-quote relative to the compositymid-quote,” where market participants react to disequilibrium in themarket price. Dynamic variables can be standardized in order to (1)remove the time of day effect, (2) better measure extreme events, and(3) allow cross-sectional analysis.

Model.

A. Size of Undisclosed Limit Order Volume.

In this section, the model is described along with empirical resultsassociated with estimating the size of the hidden volume and itslocation (placement) between the spread are examined. To achieve thisgoal, all trades that have been executed through undisclosed limitorders and their associated market conditions are identified. Becausemodeling the discrete choice of placing a hidden versus a visible limitorder is desired, a probability regression model that maps trade volumewith market conditions is used.

Different trading horizons (trading instantaneously, or within a 1-, 2-,3-, 4-, or 5-minute period) can be used. A regression model that onlyuses the hidden trade volume that is actually executed would produceestimators which are biased downward. To correct that aspect, necessarycensoring conditions are specified.

The model was evaluated and stylized facts were identified by (1)examining the prior belief and matching it with the empirical results todetermine whether these results are consistent across all liquiditygroups and (2) estimating McFadden's LRI to approximate a pseudo R² forassessing the goodness of fit.

With reference to FIG. 11, a method for evaluating a model foridentifying hidden order volume may include a step of comparing hiddenorder volume for different trading horizons and/or intervals S11-1. Suchintervals may be, for example, 1-, 2-, 3-, 4-, or 5-minute periods orinstantaneous. Then, for each interval, inferred hidden order volume andtrading conditions (explanatory variables) are determined in step S11-3.The inferred hidden order volume in compared with a historical volumepattern in step S11-5. The model's strength is then evaluated in stepS11-7. The evaluation step may include examining the prior belief andmatching it with the empirical results to see if the results areconsistent across liquidity groups. The evaluation step may also includedetermining the R² for assessing the goodness of fit.

Some stylized facts relate to modeling hidden volume. For example, theeffective spread and volatility measures capture the level offront-running and any abnormal market movement which could be associatedwith asymmetric information, “herding,” market corrections, orshort-term movements. Less than normal effective spread indicates thatmany market participants are front-running and hence, to camouflage someof the liquidity demand, the hidden volume would be greater. As forvolatility, high volatility reflects the market uncertainty and thepossibility of hidden volume being executed away from the mid-quote.With high volatility levels, a market participant is expected to placemore hidden volume, since the probability for being executed increasesand no information or strategy is revealed to the market. A largerabsolute (daily spread) for a stock is associated with more hidden ordervolume. Liquidity providers might hide more hidden volume for stocksthat have larger spreads because the likelihood of being front-runincreases. When more limit orders are place, more hidden order volume isexpected as market participants are more actively involved in the marketand gaming for asymmetric information.

Table 2 below shows a subset of the variables used in the model forpredicting hidden sell limit order volume. The numbers in parenthesesare the standard errors for the parameters. As shown in Table 2, thecoefficients associated with effective spread are negative and thecoefficients associated with volatility are positive.

TABLE 2 Standardized Addition Lagged Addition between and GoodnessHidden Mid-Quote less at the best Mid-Quote Effective Liquidity of FitR² Volume −1 0 Cancellation Bid and Ask Volatility Spread 0-2 0.050.1807 −2.9563 −1.2840 0.2043 0.2155 0.0205^(ns) −0.0064^(ns) (0.0151)(0.2336) (0.1650) (0.0523) (0.0588) (0.0763) (0.0783) 3 0.05 0.1233−0.9911 −2.9905 0.4151 0.2096 0.1557 −0.1923 (0.0112) (0.1329) (0.1888)(0.0386) (0.0425) (0.0541) (0.0553) 4 0.07 0.1072 −0.9270 −0.3364 0.13020.1057 0.1059 −0.0477 (0.0077) (0.0585) (0.0427) (0.0113) (0.0116)(0.0172) (0.0150) 5 0.08 0.1746 −0.5122 −0.2447 0.0857 0.0464 0.0420−0.0613 (0.0063) (0.0316) (0.0063) (0.0055) (0.0055) (0.0076) (0.0060) 60.08 0.2037 −0.2909 −0.0985 0.0696 0.0429 0.0424 −0.0323 (0.0043)(0.0171) (0.0120) (0.0029) (0.0030) (0.0019) (0.0030) 7 0.08 0.1387−0.2429 −0.1146 0.0350 0.0326 0.0328 −0.0236 (0.0047) (0.0144) (0.0098)(0.0022) (0.0023) (0.0013) (0.0021) 8 0.08 0.1633 −0.1931 −0.0872 0.02350.0294 0.0179 −0.0172 (0.0039) (0.0134) (0.0091) (0.0015) (0.0016)(0.0022) (0.0013)  9-10 0.06 0.3164 −0.0868 −0.0145 0.0119 0.0128 0.0091−0.0070 (0.0033) (0.0097) (0.0057) (0.0008) (0.0010) (0.0012) (0.0006)

For the variable MID-QUOTE, a 1 is assigned if ARCA's mid-quote isgreater than that of the composite mid-quote, a 0 is assigned if themid-quote is equal, and a −1 is assigned otherwise. The coefficientvalues with the superscript ns indicate that these numbers are notsignificant at the 95% confidence level. Variables are standardized bytheir corresponding historical 3 month means and standard deviations,i.e.

$X_{({standard})} = \frac{x - \overset{\_}{x}}{\sigma(x)}$where x is the mean and a σ(x) is the standard deviation of x.

Market participants can monitor the changes in the shape of the limitorder book and track order additions, cancellations, depth, previous15-seconds mid-quote returns, and the misalignment of the mid-quoteassociated relative to the composite market. These variables act as thefrontline variables to capturing market dynamics and participants'gaming/strategy. The results suggest that more additions thancancellations of limit orders is a signal that there are players in themarket that hope that such actions stimulate the market, perhaps toattract the market towards their undisclosed volume.

When the mid-quote is misaligned and the ECN's mid-quote is less thanthe composite mid-quote price, the expected buy hidden limit ordervolume will be less than that of an ECN which has a mid-quote that isequal or even greater that the composite mid-quote price (exemplary ECNsinclude Archipelago, INET, and Brut). In other words, it has beendetermined that hidden buy (sell) limit order volume follows the ECNwith the highest (lowest) mid-quote price.

Apart from these variables, the previous hidden volume executed isexamined. At first glance, one might dismiss this variable as beinginvisible and hence not a reliable explanatory variable, but this wouldbe mixing the concept of hidden with that of invisible. After anexecution against hidden volume takes place, there is a telltale tradetick which is printed. Research indicates that if hidden volume isfound, there is a good chance that there will be more hidden volume—thatis, Lagged Hidden Volume.

Certain stylized facts may be discerned. For example, when only absolute(daily) spread is considered, larger absolute spread for a stockindicates greater hidden order volume. Liquidity providers might hidemore hidden volume for stocks that have larger spreads because thelikelihood of being front-run increases. When considering only limitorder placements, when more limit orders are placed, more hidden ordervolume is expected as market participants are more actively involved inthe market and gaming for asymmetric information.

B. Location of Undisclosed Limit Order Volume

In the previous section, the size of hidden volume that is assumed to belocated between the best bid and ask was modeled. In this section, it isdescribed how the location of this volume between the best bid and askcan be estimated according to an embodiment of the present invention. Toachieve this goal, the spread can be divided into uniformly spacedregions and the explanatory variables are used to estimate theprobability that an order is placed in that region.

The premise is that market participants observe the market conditionsand from that, decide where to place hidden volume. Hence, changes inthe state of the limit order book cause participants to reevaluate theirplacement strategies. It is assumed that the “fundamental” factors,absolute historical (e.g. intra-day) spread (in cents), and volatilitycontribute to identifying where hidden orders are being placed on thebook. The assumption is that placement is based on perceived marketconditions such as absolute spread and volatility. The model maps thelocation of a hidden order with existing market conditions.

Table 3 discloses a subset of the variables used in the model forpredicting the location of sell limit order volume according to anaspect of the present invention. Table 3 gives a brief relationshipbetween a few market variables and the placement of hidden volume.

TABLE 3 Standardized Addition between Good- Return in and at the ness oflast 15- Addition less best Bid Imbalance Liquidity Fit R² secondsCancellation and Ask in Depth 0-2 0.18 −0.0425^(ns) −0.1120 0.2322−0.0878^(ns) (0.0373) (0.0460) (0.1126) (0.0673) 3 0.19 −0.0854 −0.06680.1050^(ns) −0.0923 (0.0430) (0.0258) (0.0707) (0.0404) 4 0.19 −0.3023−0.0719 0.1584 −0.1864 (0.0449) (0.0194) (0.0476) (0.0306) 5 0.20−0.2860 −0.1125 0.0274 −0.0172^(ns) (0.0590) (0.0160) (0.0516) (0.0254)6 0.20 −0.3757 −0.0894 0.1501 −0.0791 (0.0502) (0.0104) (0.0323)(0.0107) 7 0.20 −0.2443 −0.0931 0.1194 −0.0964 (0.0571) (0.0108)(0.0352) (0.0187) 8 0.23 −0.6894 −0.1184 0.2262 −0.0266 (0.0569)(0.00781) (0.0258) (0.0130) 9-10 0.19 −0.7267 −0.0963 0.1192 −0.0334(0.0589) (0.00444) (0.0141) (0.0335)

The numbers in parentheses are the standard errors for the parameters.The coefficient values with the superscript ns indicate that thesenumbers are not significant at the 95% confidence level.

All variables were standardized by their corresponding historical 3months means and standard deviations, i.e.

$X_{({standard})} = \frac{x - \overset{\_}{x}}{\sigma(x)}$where x is the mean and σ(x) is the standard deviation of x.

The variable “Return in last 15-second” is the time weighted percentagemid-quote return within the previous 15 seconds prior to execution.

If stocks in Liquidity Group 8 are examined and the bid-ask spread isdivided into six equally sized groups, then FIG. 4 illustrates howplacement of hidden volume changes with the spread where region 1includes the best ask price and region 6 includes the region prior tobest bid price. As spread increases beyond its normal levels, hiddenvolume is more likely to be redistributed within the spread. Thispattern holds true across all liquidity groups.

Thus, according to embodiments of the invention, a method of creating ahidden order location model, referring to FIG. 9, may include steps ofdetermining the location of each observed (buy) hidden limit order S9-1,i.e.,

-   -   Region 1={bid}    -   Region 2=(bid, bid+0.2·(ask−bid)]    -   Region 3=(bid+0.2·(ask−bid), bid+0.4·(ask−bid)]    -   Region 4=(bid+0.4·(ask−bid), bid+0.6·(ask−bid)]    -   Region 5=(bid+0.6·(ask−bid), bid+0.8·(ask−bid)]    -   Region 6=(bid+0.8·(ask−bid), ask);        determining market and trading conditions at the time of each        observed hidden order (explanatory variables) S9-3; estimating        probability model of order placement S9-5; and evaluating the        model's strength S9-7. The step of evaluating the model's        strength may include examining the prior belief and matching it        with the empirical results to see if the results are consistent        across liquidity groups and determining R² for assessing the        goodness of fit.

When considering certain stylized facts apart from others, certainconclusions may be drawn. For example, if only considering increasingmid-quote volatility, it is expected that an investor is more willing toplace hidden limit orders within the spread. Also, market participantswill place more hidden volume inside the spread since no information orstrategy is revealed to the market. If only considering increasingintra-day (standardized) spread, an investor is more willing toredistribute hidden order placement within the spread. Also, whenconsidering only limit order placement, if more limit orders are beingplaced, more hidden order volume inside the spread is expected. Placinghidden limit orders inside the spread camouflages one's liquidity demandand thus protects against other market participants who might stepahead.

C. Model Development

With reference to FIG. 12, a flow chart of a method for creating a modelfor calculating the probability, volume, and/or placement of a hiddenorders is shown, according to an embodiment of the present invention.Processing begins at step S12-1, wherein real-time trading messages canbe obtained or received as already discussed above in the “Data”section. From the order data, a trade may be classified as visible wherethe trade can be matched to a limit order message in step S12-3 while atrade which cannot be matched with a limit order message is classifiedas hidden in step S12-5. The side of a trade classified as hidden isdetermined in step S12-7. Trade classification and side determinationare discussed above in the “Data” section.

In step S12-9, tradable assets can be grouped into liquidity groupsbased upon the median trade volume of the asset during a pre-determinedliquidity period. A liquidity period may be, for example, the 21-dayperiod coinciding with the first 21 days of the real-time tradingmessages.

In step S12-11, one or more market conditions can be calculated for eachtradable asset over a pre-determined trading horizon. Market conditionsmay include, for example, effective spread, mid-quote volatility,additions between best bid and ask, average first level depth, orderplacements, order cancellations, and additions less cancellations. Thetrading horizon may be, for example, 1-, 2-, 3-, 4-, or 5-seconds orinstantaneous.

In step S12-13, a coefficient is calculated for each liquidity group andeach market condition, which associates the market condition with hiddentrade volume compared to visible trade volume and hidden trade locationcompared to visible trade location. The coefficients can be stored in atable of coefficients, such as in a database or other memory device. Thetable of coefficients, as already described above, can be utilized as amodel for estimating current hidden liquidity in a trade forum basedupon current market conditions.

Thus, a coefficient can be used to quantize the degree to which one ormore market conditions can relate to hidden order volume and or locationfor tradable assets. Coefficients may also be associated with liquiditygroups, as described above. The model (e.g., coefficients) can then beapplied to real-time data to estimate hidden liquidity.

Testing Model.

To examine the strength of the model in predicting the hidden volume andits placement on the order book, all (partial) executions that have thesame sign (buy or sell) and occur around the same time on ARCA wereaggregated. For each of these trade clusters, the existing marketconditions were identified and saved and the cluster volume, theshare-weighted average execution price, and the average execution pricethat is derived from the observed unadjusted limit order book at thestart of the cluster execution were calculated.

The difference between the limit order book's perceived execution pricev_(i) and the actual execution price p_(i) is referred to as the VirtualPrice Error v_(i)−p_(i). Virtual Price Errors are typically positive andgive a first impression about the usability of the displayed limit orderbook alone.

Next, the limit order book can be reconstructed based on the prevailingmarket conditions using the models that have been discussed insubsections A and B above, and the estimated undisclosed limit ordervolume at the appropriate price levels is included. Based on theadjusted limit order book, the estimated execution price v_(i) ^(new)and the New Virtual Price Error v_(i) ^(new)−p_(i), can be determined.

The above procedure enables: a) having a one-to-one comparison betweenactual and estimated prices, and b) evaluating the superiority of theadjusted limit order book over the unadjusted limit order book. Toassess accuracy, varying scenarios can be studied for each liquiditygroup, considering different Time Of Day and different levels ofVolatility, Spread, or Limit Order Volume Activity. More precisely, foreach liquidity group and scenario, the average Virtual Price Error andaverage New Virtual Price Errors can be computed for all subgroups ofeach scenario.

FIG. 5 shows the graphical comparison between the average Virtual PriceError and average New Virtual Price Error for all stocks that have beenclassified in Liquidity Group 2. The trading day can be broken-up intoseventy-eight 5-minute bins and the average Virtual Price Error andaverage New Virtual Price Error in each of these subgroups arepresented. So as to capture the Virtual Price Error distribution, the 5%and 95% levels can also be graphed. On average, there is an error ofapproximately 5-cents difference between what a trader would believe tobe the instantaneous trade execution price if he only looks at thedisplayed limit order book, and the actual execution price. Thatdisparity is eliminated when the model is used to adjust for the hiddenvolume. Similar results hold for all other examined scenarios which, forbrevity, are omitted here.

As shown in FIG. 10, the performance of a model may be evaluated byusing virtual price error computations. Steps in a method of evaluatinga model include creating trade clusters for “out of sample data” 510-1,where a trade cluster is an accumulation of (partial) executions withina short time-frame (e.g. one month) on the same side. Virtual priceswill be computed by reference to an index i, where i indexes the tradecluster. The index i is set to 1 in step S10-3. Next, the marketconditions around the execution time of trade cluster i are determinedin step S10-5 and the average execution price of that trade cluster iscomputed in step S10-7. In step S10-9, the limit order book's perceivedexecution price is computed and in step S10-11, the “true” limit order,book based on the market conditions, is reconstructed using the model'sexecution price. Then, the virtual price error and new virtual priceerror are computed in steps S10-15 and S10-17. The index i isincremented in step S10-19 and subsequently compared to the number oftrade clusters to determine whether additional virtual price errors mustbe computed. In step S10-21, the virtual price errors may be subdividedinto different scenarios and the averages compared for each group.

Scenarios may be subdivided by time of day, volatility, spread, limitorder volume activity and other factors. The method of FIG. 10 permits aone-to-one comparison between actual and estimated execution prices andevaluation of the superiority of the adjusted limit order book over theunadjusted limit order book.

Applications.

In this section, the practical importance of the model of the presentinvention is described and illustrated. A static example associated withplacing a market order is created examine both the cost and price impactassociated with executing the order instantaneously and within a 2- and5-minute bin period are examined. The price impact PI_(i) of a marketorder i is defined as the difference between the last execution pricep_(i) ^(final) and the mid-quote m_(i) immediately prior to the marketorder i. Similarly, the cost C_(i) of a market order i is defined as thedifference between the share-weighted average execution price P _(i) andthe mid-quote m_(i) immediately prior to the market order i. Moreprecisely,PI _(i)=δ_(i)·(p _(i) ^(final) −m _(i))andC _(i)=δ_(i)·( p _(i) −m _(i)),where δ_(i)=1 for a buy market order and δ_(i)=−1 otherwise.

FIG. 1 illustrates that executing a buy market order of 1,000 shares ofthe company, Argonaut Group Inc. would have a price impact of $0.10 andthe cost per share would be $0.05. For illustration purposes, it isassumed that at 10:40 am, Argonaut Group Inc. is very actively tradedwith an effective spread of one deviation less than average andvolatility being one half of a deviation higher than normal. Moreover,it is assumed that in the previous 5-minute bin, of the 1,000 sharestraded, 30% are classified as being hidden shares. From the specifiedmarket conditions, it is estimated that there will be around 60 hiddenshares instantaneously available between the best bid and ask and 147and 280 hidden shares of sell limit orders within the next 2 and 5minutes, respectively. Table 4 gives the complete breakdown.

TABLE 4 INSTANTA- 2- 5- PROBA- PRICE NEOUS MINUTES MINUTES BILITY $35.003 7 13 0.046319 $35.01 2 4 8 0.027683 $35.02 5 12 23 0.080532 $35.03 615 29 0.105157 $35.05 43 109 207 0.740309

Given the existing trading conditions for Argonaut Group Inc. at 10:40am, Table 4 presents the amount of hidden sell limit order volume andits location for different execution horizons. The estimated hiddenvolume is expected to be available for a market order being executedinstantaneously, within 2, or 5 minutes. If there is hidden volume,column “PROBABILITY” shows the likelihood that hidden volume is locatedat that price.

Next, the location of the estimated hidden sell limit order volume canbe estimated. That is, the price level at which one could expect theundisclosed sell limit orders. Using the probability model discussedabove subsection B of the “Model” section, the probability associatedwith each price level between the best bid and ask is estimated.

Given the market conditions for Argonaut Group Inc. at 10:40 am, Table 4shows that there is approximately 4.6% of hidden sell limit order volumelocated at the price level $35.00 and that 15.45% of total hidden selllimit order volume is available at or below $35.02. As for the best askprice ($35.05), there is approximately 74% of the total hidden selllimit order volume located at that level. If the limit order book isreconstructed to include the hidden volume (the probabilities aremultiplied by the total hidden sell limit order volume), the price pershare traded for the instantaneous trade model (with the assumption oflocating 59 shares) is $35.065 and the cost is $0.045, which is lowerthan the estimated cost for the unadjusted book. The price impactremains as $0.10.

FIG. 6 is a graphical representation of trading horizon, hidden selllimit order volume, and average execution price. FIG. 6 shows theaverage execution price based on the unadjusted (static) limit orderbook in comparison to the adjusted book that takes into account tradinginstantaneously and with 1-, 2-, 3-, 4-, and 5-minute horizon. Astrading horizon increases and the market players execute against theestimated volume within the next 5 minutes, the average expectedexecution price falls to $35.052 and the expected price impact decreasesto $0.05.

While market venues strive to achieve greater transparency by offeringmarket data products with more granular and current information, marketparticipants, in their demand for minimal information leakage, continueto hide their trading intent by placing hidden limit orders. Thisconflict between market transparency and traders' secrecy complicatesthe tasks of algorithmic trading systems of seeking out both liquidityand best execution, and complicates the tasks of the market participantby obscuring the true liquidity of the market.

The rising popularity of placing undisclosed limit orders instead ofdisplayed limit orders, has greatly limited the usefulness of the limitorder book when it comes to transparency of market participants'actions. It has been shown that using a “simple” limit order book isinsufficient for estimating true liquidity and transaction costs.Furthermore, utilizing an analysis of the “simple” limit order book andignoring the undisclosed limit order volume actually alter the executionoptimization and transaction and opportunity cost reduction, with a biastowards lower available liquidity and higher transaction costs.

However, it can easily be inferred from the results that ignoring theprobability of undisclosed volume within the spread greatly limits (atbest) the ability of algorithmic trading systems and smart order routingsystems to find the best execution price for market orders. Algorithmictrading systems must either uniformly search across different marketvenues (at a great opportunity cost) or devise smarter ways to seek outavailable liquidity. So-called ‘smart’ order routing systems that do nottake into account the probability of undisclosed volume within thespread aren't smart.

The present invention provides market participants systems and methodsfor monitoring the limit order book for liquidity. The Effective Spreadis negatively correlated to the hidden liquidity and the Mid-QuoteVolatility, Additions Between Best Bid And Ask, and the Additions LessCancellations are all positively correlated to hidden volume. Althoughthese facts do not permit a reconstruction of the “real” book, they arenonetheless useful in getting at least a sense of the overall hiddenliquidity, if not also its size and location.

The present invention is not limited to the foregoing disclosure andstylized facts. It can be used to enhance the existing picture of thelimit order book by synthesizing the “real” limit order book based onthe probability of hidden volume, including its location (in the book),size, and venue. The major implications of utilizing this extrainformation are twofold and apply both to automated trading systems andmarket participants' strategies.

For example, in algorithmic trading systems and smart routing systems itwould be obvious that given equal price and liquidity across multiplevenues, the best choice of which venue to route to would be the one withthe highest probability of undisclosed volume within the spread; suchsystems would be considered to be “smart”. For market participants thisenhanced book information can be used to guide a liquidity trader to thebest sources of liquidity and could potentially be used to driveenhanced limit order trading models. By utilizing this enhanced book inchoosing to place a limit order, and in selecting its price, size, time,venue, and whether or not it should be displayed, the market participanthas a more realistic view of how others will respond to his action.

In accordance with method of estimating hidden volume embodying anaspect of the invention, and with reference to FIG. 8, there are thefollowing steps: Data are captured in real-time using Level 2 data fromeach exchange (e.g. NYSE, ARCA, ITCH, BATS) in step S8-1. Then, existinglimit order books are updated in memory (for each exchange andaggregated/consolidated) in step S8-3. Recent book activity on eachexchange is stored in memory and aggregated/consolidated (for example,limit order cancellations, hidden order volume activity in the last 30seconds) in step S8-5. Relevant historical-based statistics areretrieved from the MD database (for example, mean and standard deviationof trading volume and hidden volume in the last 5 minutes) in step S8-7.The estimated hidden volume is calculated on the fly between bid and askon each trading venue and aggregated in step S8-9. Determinations ofwhich exchange which has best price and deepest book (including visibleand hidden) and the aggressiveness of trade given the current liquidityin the market are made in step S8-11.

Referring now to FIG. 7, a schematic diagram of an exemplary system 720that can be configured to perform aspects of the present inventiondescribed above, such as, but not limited to, processes for estimatingthe probability of hidden market orders according to an embodiment ofthe present invention is shown. The system 720 can include a server 722in communication with one or more user workstations 724, for example viaa direct data link connection or a network such as a local area network(LAN), an intranet, or internet. The server 722 and the work stations724 can be computers of any type so long as they are capable ofperforming their respective functions as described herein. The computerscan be the same, or different from one another, but preferably each haveat least one processor and at least one memory device capable of storinga set of machine readable instructions (i.e., computer software)executable by at least one processor to perform the desired functions,where by “memory device” is meant any type of media or device forstoring information in a digital format on a permanent or temporarybasis such as, for example, a magnetic hard disk, flash memory, anoptical disk, random access memory (RAM), etc.

Computer software stored on the server (“server software”), whenexecuted by the server's processor, causes the server 722 to communicatewith the workstations 24 and one or more sources 726 of financial data,such as data vendors, that offer real-time securities data in anelectronic format. The server software, when executed by the server'sprocessor, also causes the server 722 to perform certain calculations,described in greater detail below, using the real-time data from thedata vendors 726, as well as estimating the probability of hidden marketorders, and providing estimated order book data for display on one ormore workstations 724.

The computer software stored on a workstation (“user software”), whenexecuted by the workstation processor, causes the workstation 724 toreceive estimated order book data from the server 722 and to display theestimated order book data to a user on a monitor. Real-time andhistorical securities data used by the system 720 to estimate an orderbook can be received from a remote source 720, such as a data vendor, orfrom a local database 730 connected to, or maintained on, the server722.

The server 722 can be located at a user's facility or at a site remotefrom the user's facility. Communication between the server 722 and thedata vendors 726 and 728 can be accomplished via a direct data linkconnection or a network, such as a LAN, an intranet, or internet. Inalternate embodiments, one or more workstations can be configured toperform the server functions such that a dedicated server is not needed.It will also be appreciated that workstations can be configured tocommunicate individually with data vendors and/or local databaseswithout being networked to a server or other workstations.

A number of embodiments of the present invention have been fullydescribed above with reference to the drawing figures. Although theinvention has been described based upon these preferred embodiments, itwould be apparent to those of skill in the art that certainmodifications, variations, and alternative constructions could be madeto the described embodiments within the spirit and scope of theinvention. For example, as explained above, numerous other analyticscould be calculated for the purpose of generating indicators of abnormaltrading conditions for a security according to the present invention.

We claim:
 1. A system for constructing an order book from displayedmarket data for a tradable asset, said system comprising one or morecomputer processors configured to: measure an effective spread of thetradable asset from displayed market data; measure a mid-quotevolatility of the tradable asset from displayed market data; measureadditions between best bid and ask of the tradable asset from displayedmarket data; measure additions less cancellations of the tradable assetfrom displayed market data; calculate, with the one or more computerprocessors, a probability of a hidden order for the tradable asset as afunction of the measured effective spread, the mid-quote volatility,additions between best bid and ask, and additions less cancellations;calculate, with the one or more computer processors, a hidden ordervolume between the best bid and ask; calculate, with the one or morecomputer processors a hidden order price; and construct an order bookfor the tradable asset that includes displayed order volume and hiddenorder volume based on said calculated probability of a hidden order,said calculated hidden order volume, and said calculated hidden orderprice.
 2. The system in accordance with claim 1 wherein the probabilityof a hidden order is also a function of the time of day.
 3. A system forconstructing an order book from displayed market data for a tradableasset said system comprising: means for measuring an effective spread ofthe tradable asset from displayed market data; means for measuring amid-quote volatility of the tradable asset from displayed market data;means for measuring additions between best bid and ask of the tradableasset from displayed market data; means for measuring additions lesscancellations of the tradable asset from displayed market data; meansfor calculating. with one or more computer processors, a probability ofa hidden order for the tradable asset as a function of the measuredeffective spread, the mid-quote volatility, additions between best bidand ask, and additions less cancellations; means for calculating, withone or more computer processors, a hidden order volume between the bestbid and ask; and means for calculating, with one or more computerprocessors, a hidden order price; and means for constructing an orderbook for the tradable asset that includes displayed order volume andhidden order volume based on said calculated probability of a hiddenorder, said calculated hidden order volume, and said calculated hiddenorder price.
 4. The system according to claim 3, further comprisingmeans for merging the calculated hidden order volume and hidden orderprice with a displayed order book.
 5. A system for creating a model forcalculating a probability and a characteristic of a hidden order for atradable asset, said system comprising one or more computer processorsconfigured to: access a plurality of electronic, level-2 tradingmessages from a trading forum for a predefined period of time, eachmessage including information about one or more orders for tradableassets or executed trades for tradable assets, said order informationincluding identification of a tradable asset, a price, and a quantity;identify executed trades from said messages; classify a trade from theidentified trades as displayed if the trade can be matched to orders insaid messages; classify a trade as hidden where said trade cannot bematched to orders in said messages; determine a side of each ordercorresponding to a trade classified as hidden; calculate, with the oneor more computer processors, a hidden trade volume and a hidden tradelocation for tradable assets based upon said classifying steps and saiddetermining step; group each tradable asset in the plurality of tradableassets into one of a plurality of liquidity groups based upon said eachtradable asset's median trade volume over a pre-determined liquidityperiod; calculate, with the one or more computer processors, for eachtradable asset in the plurality of tradable assets at least one marketcondition; and calculate, with the one or more computer processors, fora liquidity group a coefficient associating the at least one marketcondition with at least one of said hidden trade volume and said hiddentrade location.
 6. The system according to claim 5 wherein thepre-determined liquidity period is a 21-day period coinciding with afirst 21-days of the plurality of trading messages.
 7. The systemaccording to claim 5, wherein the market condition comprises at leastone of the an effective spread, a mid-quote volatility, additionsbetween best bid and ask, average first level depth, order placements,order cancellations, and additions less cancellations over apre-determined trading horizon.
 8. The system according to claim 5wherein the number of liquidity groups is
 11. 9. The system of claim 5wherein the real-time trading messages are obtained from ARCA ComstockL1 and L2 feeds.
 10. The system of claim 5 wherein the trading messagesare obtained from a direct exchange L2 feed.
 11. The system of claim 5wherein at least one coefficient x is standardized as X_((standard)) byits corresponding mean and standard deviation over a pre-determinedprior standardization period.
 12. The system of claim 11 wherein thepre-determined prior standardization period is the prior three months.13. The system of claim 12, wherein the standardized coefficientX_((standard)) is computed using the formula$X_{({standard})} = \frac{x - \overset{\_}{x}}{\sigma(x)}$ where x isthe mean over the pre-determined prior standardization period and σ(x)is the standard deviation of x over the pre-determined priorstandardization period.
 14. The system of claim 5, wherein the one ormore computer processors are further configured to estimate a McFadden'sLRI to approximate a pseudo R² for assessing the goodness of fit of acoefficient.